Every exercise has a failure point - a weakness in the exerciser that limits his or her ability to continue to execute it.
So what does that mean when you program an exercise into your plan that has a specific point of failure?
I believe it means that you've prioritized that point of failure.
Your point of failure is your priority. Whatever fails first, and causes you to lose good form and stop, or just plain fails, is what you are prioritizing. Regardless of what the exercise is supposed to do, what it's doing is working on that specific weakness - or at the very least exposing it.
For example, is a deadlift a leg exercise or a back exercise? It's both, but if you fail because of tired legs it's not really working your back to the utmost, so your legs are your failure point.
You can use this in training for a variety of purposes.
For example, a person with poor shoulder endurance doing suspended pushups (with rings, say, or any similar training device). What will give out first is the ability of the shoulders to stabilize the body's position. So even if the triceps and chest can crank out more reps, the shoulders can't keep the rings in position and you cannot continue. This oddly makes it safer for someone with shoulder stability issues than regular pushups, because the exerciser must stop when he or she is unable to stabilize the rings.
Another example is a farmer's walk. Does the weight fall out of your hands due to a weak grip? Then, ultimately, you've gotten some ab and leg and back work but your grip is getting the biggest workout. Your grip has become the point of priority, and it's worth considering this exercise as slotting in where you'd do grip work. Same with, say, fat grip work - you add it in to prioritize grip over anything else.
Your point of failure on an exercise is a "weak point" but it's also your priority.